WebOct 5, 2024 · I have a question regarding Goormaghtigh conjecture on the Diophantine equation $$\frac{x^m-1}{x-1}=\frac{y^n-1}{y-1}.$$ Suppose that a positive integer $N$ … WebIn mathematics, the Goormaghtigh conjecture is a conjecture in number theory named for the Belgian mathematician René Goormaghtigh.The conjecture is that the only non-trivial integer solutions of the exponential Diophantine equation = satisfying x > y > 1 and n, m > 2 are (x, y, m, n) = (5, 2, 3, 5); and(x, y, m, n) = (90, 2, 3, 13).
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WebJun 1, 2024 · Horn conjecture, Goormaghtigh conjecture. 1. 2 GARETH A. JONES AND ALEXANDER K. ZVONKIN. Unfortunately, this result does not tell us when the degree m in (b) is prime. Indeed, it is unknown. WebThanks to everyone who commented! I'll go ahead and answer my own question. I found a wikipedia page on this exact problem, where it is labelled the Goormaghtigh conjecture, and is listed under the wiki page of unsolved problems in number theory.So it seems that if anyone knew how to solve this equation that would be mighty impressive. openespecially
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WebApr 14, 2024 · The Goormaghtigh conjecture explores the Diophantine equation of the form a b − 1 a − 1 = c d − 1 c − 1, where a > c > 1 and b, d > 2, where a, b, c, d ∈ Z. A … WebThe twin-prime conjecture (also known as Polignac’s conjecture, 1846) states that there are infinitely many twin primes (pairs of primes that differ by 2; for example, 3 and 5, 5 and 7, 11 and 13, and ... Webstandard conjectures about algebraic cycles are several conjectures describing the relationship of algebraic cycles and Weil cohomology theories. One of the original applications of these conjectures, envisaged by Alexander Grothendieck, was to prove that his construction of pure motives gave an abelian category that is semisimple. iowa shooting update